I think there was such a planet mentioned in one of Asimov's Foundation books. It was a pleasant resort planet, as I recall, with the settlements around the habitable ring having constantly perfect weather.
edit: I looked it up: Radole, in Second Foundation. Asimov coined the term "ribbon world" to describe planets like this where the habitable zone forms a ribbon.
edit: I looked it up: Radole, in Second Foundation. Asimov coined the term "ribbon world" to describe planets like this where the habitable zone forms a ribbon.